Bio

Anna Seigal is an Assistant Professor of Applied Mathematics in the School of Engineering and Applied Sciences at Harvard, and an Affiliate in the Department of Statistics. Her research is in applied algebra. She was previously a Junior Fellow at the Society of Fellows at Harvard University. Before that, she held a Hooke Research Fellowship in the Mathematical Institute at the University of Oxford and a Junior Research Fellowship at The Queen's College. She received her PhD from UC Berkeley in 2019. She is a recipient of the SIAM Richard C. DiPrima Prize and an Alfred P. Sloan Research Fellowship in Mathematics.

Group

Graduate Students:

Álvaro Ribot
Kexin (Ada) Wang

Postdocs:

Aida Maraj
Chiara Meroni

Senior theses:

Paula Leyes Carreno: Learning Linear Causal Representations Using Higher-Order Cumulants, 2024.

Group photos:

Research Articles

Preprints:

32. Decomposing tensors via rank-one approximations (with Alvaro Ribot, Emil Horobet, and Ettore Teixeira Turatti), arXiv:2411.15935.

31. A Real Generalized Trisecant Trichotomy (with Kristian Ranestad and Kexin Wang), arXiv:2409.01356.

30. Linear causal disentanglement via higher-order cumulants (with Paula Leyes Carreno and Chiara Meroni), arXiv:2407.04605.

29. Contrastive independent component analysis (with Kexin Wang and Aida Maraj), arXiv:2407.02357. [code]

28. Identifiability of overcomplete independent component analysis (with Kexin Wang), arXiv:2401.14709.

27. Complete collineations for maximum likelihood estimation (with Gergely Bérczi, Eloise Hamilton, and Philipp Reichenbach), arXiv:2311.03329.

26. Supermodular Rank: Set Function Decomposition and Optimization (with Rishi Sonthalia and Guido Montúfar), arXiv:2305.14632.

25. Deciphering causal genomic templates of complex molecular phenotypes (with Salil Bhate and Juan Caicedo), bioRxiv:2022.08.15.503769.

Publications:

24. Multilinear Hyperquiver Representations (with Tommi Muller and Vidit Nanda), Foundations of Computational Mathematics 2025. [arXiv] [pdf] [Tommi's talk]

23. A Bridge between Invariant Theory and Maximum Likelihood Estimation (with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach), SIAM Review 2024, Vol. 66, No. 4 721–747. [pdf] [sigest] [news story]

22. Differential equations for Gaussian statistical models with rational maximum likelihood estimator (with Carlos Améndola, Lukas Gustafsson, Kathlén Kohn, and Orlando Marigliano), SIAM Journal on Applied Algebra and Geometry 2024, Vol. 8, No. 3. [arXiv] [pdf] [code]

21. Rectifiable paths with polynomial log-signature are straight lines (with Peter Friz and Terry Lyons), Bulletin of the London Mathematical Society (2024) 1-13. [arXiv] [pdf]

20. Symmetries in Directed Gaussian Graphical Models (with Visu Makam and Philipp Reichenbach), Electronic Journal of Statistics 2023, Vol. 17, No. 2, 3969-4010. [arXiv] [pdf] [code]

19. Linear Causal Disentanglement via Interventions (with Salil Bhate, Chandler Squires, and Caroline Uhler), Proceedings of the 40th International Conference on Machine Learning (ICML 2023), PMLR 202, 2023. [arXiv] [pdf] [code]

18. Lower bounds on the rank and symmetric rank of real tensors (with Kexin Wang), Journal of Symbolic Computation 118 (2023) 69–92. [arXiv] [pdf] [code]

17. Principal Components along Quiver Representations (with Heather Harrington and Vidit Nanda), Foundations of Computational Mathematics 23 (2023) 1129–1165. [arXiv] [pdf]

16. A blood atlas of COVID-19 defines hallmarks of disease severity and specificity (as part of 100+ author Covid-19 Multi-omics Blood Atlas (COMBAT) Consortium), Cell 185 (2022) 916–938. [medRxiv]

15. Toric Invariant Theory for Maximum Likelihood Estimation in Log-linear Models (with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach), Algebraic Statistics 12 (2021) no. 2, 187-211. [arXiv] [pdf]

14. The Maximum Likelihood Degree of Linear Spaces of Symmetric Matrices (with Carlos Améndola, Lukas Gustafsson, Kathlén Kohn, and Orlando Marigliano), Le Matematiche 76 (2021) no. 2, 535-557. [arXiv]

13. Invariant Theory and Scaling Algorithms for Maximum Likelihood Estimation (with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach), SIAM Journal on Applied Algebra and Geometry 5 (2021) no. 2, 304-337. [arXiv] [pdf] [case study]

12. Ranks and Singularities of Cubic Surfaces (with Eunice Sukarto), Le Matematiche 75 (2020) no. 2, 575-594. [arXiv] [pdf]

11. Ranks and Symmetric Ranks of Cubic Surfaces, Journal of Symbolic Computation 101 (2020) 304-317. [arXiv] [pdf]

10. Learning Paths from Signature Tensors (with Max Pfeffer and Bernd Sturmfels), SIAM Journal on Matrix Analysis and Applications 40 (2019) no. 2, 394-416. [arXiv] [pdf] [code]

9. Tensor clustering with algebraic constraints gives interpretable groups of crosstalk mechanisms in breast cancer (with Mariano Beguerisse-Díaz, Birgit Schoeberl, Mario Niepel and Heather Harrington), Journal of the Royal Society Interface 16 (2019) no. 151, 20180661. [arXiv] [pdf] [News story]

8. Duality of Graphical Models and Tensor Networks (with Elina Robeva), Information and Inference: A Journal of the IMA, iay009. [arXiv] [pdf]

7. Mixtures and products in two graphical models (with Guido Montúfar), Journal of Algebraic Statistics 9 (2018) no. 1, 1-20. [arXiv] [pdf]

6. Gram Determinants of Real Binary Tensors, Linear Algebra and its Applications 544 (2018) 350-369. [arXiv] [pdf]

5. Real Rank Two Geometry (with Bernd Sturmfels), Journal of Algebra 484 (2017), 310-333. [arXiv] [pdf]

4. Does Antibiotic Resistance Evolve in Hospitals? (with Portia Mira, Bernd Sturmfels and Miriam Barlow), Bulletin of Mathematical Biology 79 (2017) 191-208. [arXiv] [pdf] [R package] [News story]

3. Singular Vectors of Orthogonally Decomposable Tensors (with Elina Robeva), Linear and Multilinear Algebra 65 (2017) no. 12, 2457-2471. [arXiv]

2. Eigenconfigurations of Tensors (with Hirotachi Abo and Bernd Sturmfels), Algebraic and Geometric Methods in Discrete Mathematics, Contemporary Mathematics 685, Amer. Math. Soc., Providence, RI (2017) 1-25.

1. Local dynamics of intersections: V. I. Arnold's theorem revisited (with Sergei Yakovenko) Israel Journal of Mathematics 201 (2014) no. 2 813-833. [arXiv] [pdf]

PhD thesis:

Structured Tensors and the Geometry of Data , 2019.

Expository Writing and Outreach

Ideas for a complex world, a public lecture I gave as part of the Oxford Mathematical Institute public lecture series, Oxford, November 2020. Featured in the Oxford Mathematics Annual Newsletter 2021.

The Algebraic Statistics of an Oberwolfach Workshop, Snapshots of modern mathematics from Oberwolfach (2018) no. 1.

Applied Algebra and Geometry: A SIAGA of Seven Pictures, also featured as a series of three articles in SIAM news: I, II, III, Spring 2016.

Picture this Maths, a joint blog with Rachael Boyd to present mathematical research centered around pictures. Featured here in the AMS Blog on math blogs.

Iwasawa Theory of Elliptic Curves with Complex Multiplication, Part III essay (master's thesis) supervised by John Coates, Cambridge, Spring 2014.

Imagining things: What do you think about, when you think about maths?, a mini documentary about mathematical thinking, directed by Richard Braham and me, Cambridge, 2013.

Conferences

Upcoming:

SIAM Conference on Mathematics of Data Science (MDS24), Atlanta, October 2024.

Workshop on Applied and Computational Algebraic Geometry, Isaac Newton Institute, Cambridge, UK, January 2024.
Workshop on Connecting Higher-Order Statistics and Symmetric Tensors, ICERM, Providence, Rhode Island, January 2024.
Algebraic Statistics and Our Changing World, IMSI, October 2023.
SIAM Conference on Applied Algebraic Geometry, TU Eindhoven, July 2023.
Workshop on Computations and Data in Algebraic Statistics, Casa Matemática Oaxaca, Mexico (online), May 2023.
Joint Mathematics Meetings, Boston, January 2023.
Algebraic Structures in Statistical Methodology, Mathematisches Forschungsinsitut Oberwolfach, December 2022.
Combinatorial, Computational, and Applied Algebraic Geometry (CCAAGS-22), University of Washington, Seattle, June 2022.
Workshop on Nonlinear Algebra and Combinatorics from Physics, Center Of Mathematical Sciences And Applications, Harvard University, April 2022.
Optimization under Symmetry Workshop, Program on Geometric Methods in Sampling and Optimization, Simons Institute for the Theory of Computing, Berkeley, November 2021.
Geometry and Learning from Data Workshop, Casa Matemática Oaxaca, Banff International Research Station, Mexico (online), October 2021.
SIAM Conference on Applied Algebraic Geometry, Texas A&M University (online), August 2021.
Applications of Rough Paths: Computational Signatures and Data Science, ICERM, Providence, RI (online), July 2021.
Real Algebraic Geometry and Algorithms for Geometric Constraint Systems Workshop, Fields Institute, Toronto (online), June 2021
Tensor Methods and Emerging Applications to the Physical Sciences, IPAM, Los Angeles (online), May 2021
~~SIAM Annual Meeting, Toronto, July 2020~~
~~Computational Algebraic Geometry Workshop, Foundations of Computational Mathematics (FoCM 2020), Vancouver, June 2020~~
~~Algebraic Structures in Statistical Methodology Workshop, Oberwolfach, Germany, March 2020~~
12th International Conference of the ERCIM Working Group on Computational and Methodological Statistics, London, December 2019
Real Applied Algebraic Geometry, TU Berlin, September 2019
SIAM Conference on Applied Algebraic Geometry, Bern, Switzerland, July 2019
Geometry of Polynomials program, Simons Institute, Berkeley, Spring 2019
Advances in Applied Algebraic Geometry conference, Bristol, December 2018
Real Algebraic Geometry and Optimization workshop, Nonlinear Algebra Program, ICERM, Fall 2018
Boltzmann Machines workshop, American Institute of Mathematics (AIM), San Jose, September 2018
SIAM Annual Meeting, Portland, July 2018
Berlin-Oxford Meeting on Applied Stochastic Analysis, Berlin, June 2018
SIAM Conference on Applied Linear Algebra, Hong Kong, May 2018
AMS Special Session on Algebraic Statistics, Northeastern University, April 2018
Joint Mathematics Meetings, San Diego, January 2018
SIAM AG Conference, Georgia Tech, July 2017
Tensors CBMS Conference, Auburn University, Alabama, July 2017
Interactions between algebra and the sciences, MPI Leipzig, Germany, May 2017
Algebraic Statistics Workshop, Oberwolfach, Germany, April 2017
Tensors: Algebra meets Numerics, MPI MiS Leipzig, Germany, December 2016
SIAM Annual Meeting, Boston, July 2016
Macaulay2 Workshop, Warwick, UK, May 2016
AMS special session on Combinatorial and Computational Commutative Algebra and Algebraic Geometry, Salt Lake City, April 2016
Workshop on Tensor Decomositions and Applications, Leuven, Belgium, January 2016
Joint Mathematics Meetings, Seattle, January 2016
Algorithms and Complexity in Algebraic Geometry reunion workshop, Simons Institute, Berkeley, December 2015
Summer Graduate School on Mathematical Topics in Systems Biology, organized by the Altchuler-Wu Lab, MSRI, Berkeley, July 2015
Workshop on Non-Linear Algebra, Berlin, Germany, May 2015
Western Algebraic Geometry Symposium, University of Idaho, October 2014
Algorithms and Complexity in Algebraic Geometry program, Simons Institute, Berkeley, Fall 2014

Activities

January 2024: I organized, with Martin Helmer, Vidit Nanda, and Yusra Naqvi, a workshop on Applied and Computational Algebraic Geometry at the Isaac Newton Institute in Cambridge, UK.

Spring 2023: I organized, with Melanie Weber, a seminar on Applied Algebra and Geometry in Harvard Applied Math.

Spring 2022: I organized, with Xiao-Li Meng, a mini-workshop on Algebraic Statistics at Harvard University.

Summer 2021: I organized, with Michael Walter, a mini-symposium at the SIAM Conference on Applied Algebraic Geometry called "Applied Invariant Theory: Statistics and Algorithms".

2020-2021: I organized, with Vidit Nanda, the Data Science seminar at the Mathematical Institute in Oxford.

Spring 2021: I gave two introductory lectures at the IPAM long program on "Tensor Methods and Emerging Applications to the Physical and Data Sciences". They were (i) From linear algebra to multi-linear algebra (ii) Tensors in statistics and data analysis.

Summer 2019: I organized, with Carlos Améndola, Joscha Diehl, and Francesco Galuppi, a mini-symposium at the SIAM Conference on Applied Algebraic Geometry, called "Signature tensors of paths".

Spring 2019: I organized a learning seminar on Applied Invariant Theory.

Summer 2018: I organized, with Elina Robeva, a mini-symposium at the SIAM Annual meeting "Theoretical Challenges of Tensor Decomposition".

Summer 2018: I organized, with Andre Uschmajew and Bart Vandereycken, a mini-symposium in the SIAM Conference on Applied Linear Algebra, called "Tensors and Multilinear Algebra".

Summer 2017: I organized, with Elina Robeva, a mini-symposium in the SIAM Conference on Applied Algebraic Geometry, called "Tensors: From Algebra to Applications".

Spring 2017: I organized the workshop Interactions between Algebra and the Sciences with Jacinta Torres.

Fall 2016: I co-organized a tensors reading group Foundational Tensor Theory with Rockford Sison.

Fall 2015: I organized a Commutative Algebra reading group.

Summer 2013: I did a research project at Imperial College, London under the supervision of Mike Levin. We analysed biological pathways associated with susceptibility to inflammatory diseases.

Summer 2012: I attended the Kupcinet-Getz Program at the Weizmann Institute in Israel, working with Sergei Yakovenko on algebraic properties of local dynamics of intersections, see here.

Teaching

Spring 2025: Algebra for Models and Data (Applied Math 106).

Fall 2023: Algebraic Fundamentals of Representing Data (Applied Math 210).

Trinity 2020: Tutorials for Statistics and Data Analysis, The Queen's College, Oxford.

Spring 2018: GSI for Math 10B with Prof. Kelli Talaska, UC Berkeley.

Spring 2017: Head GSI for Math 10B with Prof. Craig Evans. A fun worksheet I made for the last class of the semester, UC Berkeley.

Spring 2016: I organized a Mathematical Biology reading group for a group of Berkeley undergraduate students.

Fall 2015: GSI for Math 10A with Prof. Richard Bamler, UC Berkeley.

Contact

Pronouns: she/her
Email: aseigal at seas dot harvard dot edu
Post: 29 Oxford Street, Pierce Hall 324, Cambridge, MA 02138

Anna Seigal

Bio